Quantile estimation for L\'evy measures

Generalizing the concept of quantiles to the jump measure of a L\'evy process, the generalized quantiles $q_{\tau}^{\pm}>0$, for $\tau>0$, are given by the smallest values such that a jump larger than $q_{\tau}^{+}$ or a negative jump smaller than $-q_{\tau}^{-}$, respectively, is expected only once in $1/\tau$ time units. Nonparametric estimators of the generalized quantiles are constructed using either discrete observations of the process or using option prices in an exponential L\'evy model of asset prices. In both models minimax convergence rates are shown. Applying Lepski's approach, we derive adaptive quantile estimators. The performance of the estimation method is illustrated in simulations and with real data.Comment: 38 pages, 1 figur

Estimation of integrated volatility of volatility with applications to goodness-of-fit testing

In this paper, we are concerned with nonparametric inference on the volatility of volatility process in stochastic volatility models. We construct several estimators for its integrated version in a high-frequency setting, all based on increments of spot volatility estimators. Some of those are positive by construction, others are bias corrected in order to attain the optimal rate $n^{-1/4}$. Associated central limit theorems are proven which can be widely used in practice, as they are the key to essentially all tools in model validation for stochastic volatility models. As an illustration we give a brief idea on a goodness-of-fit test in order to check for a certain parametric form of volatility of volatility.Comment: Published at http://dx.doi.org/10.3150/14-BEJ648 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Pre-Darwinian species change: reincarnation and transformism in George Sand’s Évenor et Leucippe

No abstract available

The Illusion of Purity:Chantal Mouffe's Realist Critique of Cosmopolitanism

Over the last 20 years, cosmopolitan theories have been benefiting greatly from the dialogue between defenders and critics of world citizenship. Yet, the decidedly polemic aspect of this debate, while allowing for intellectual progress, is also responsible for overdrawn generalizations. Instead of entering into the debate directly, this article attempts to refute a specific anti-cosmopolitan claim raised by Chantal Mouffe. Her realist objection to cosmopolitanism, derived from the conceptual framework of agonistic pluralism, is mistaken at a crucial point: a firm dichotomy between politics and morality cannot provide an alternative to theories of world citizenship, because Mouffe’s embrace of multipolarity as a principle of global politics must equally appeal to a set of universal norms governing international relations. This article argues that even the realist model of multipolarity needs to conceive of a minimal morality to create the symbolic ground on which various power centres can be held accountable